Specification Of State Research Articles

Electronic Excitations in Solution: The Interplay between State Specific Approaches and a Time-Dependent Density Functional Theory Description.

We critically analyze the performances of continuum solvation models when coupled to time-dependent density functional theory (TD-DFT) to predict solvent effects on both absorption and emission energies of chromophores in solution. Different polarization schemes of the polarizable continuum model (PCM), such as linear response (LR) and three different state specific (SS) approaches, are considered and compared. We show the necessity of introducing a SS model in cases where large electron density rearrangements are involved in the excitations, such as charge-transfer transitions in both twisted and quadrupolar compounds, and underline the very delicate interplay between the selected polarization method and the chosen exchange-correlation functional. This interplay originates in the different descriptions of the transition and ground/excited state multipolar moments by the different functionals. As a result, the choice of both the DFT functional and the solvent polarization scheme has to be consistent with the nature of the studied electronic excitation.

Excited states of ladder-type π-conjugated dyes with a joint SOS-CIS(D) and PCM-TD-DFT approach.

First-principle simulations aimed at accurately reproducing the excited state properties of a large series of ladder-type π-conjugated organic molecules containing heteroatoms (Si, S, B, O, and N) have been performed. In particular, time-dependent density functional theory (TD-DFT) calculations relying on several global and range-separated hybrid functionals have been carried out in conjunction with three variations of the polarizable continuum model (PCM), namely, the linear-response (LR), corrected linear-response (cLR), and state-specific (SS) approaches. For this series of molecules, similar to many borate derivatives, the cLR-PCM-TD-M06-2X approach can be used to reproduce the auxochromic effects that tune the 0-0 energies. However, TD-DFT yields rather large absolute deviations with respect to the experimental 0-0 energies. These systematic errors can be reduced by more than 0.1 eV when scaled opposite spin-configuration interaction singles with a double correction [SOS-CIS(D)] vertical calculations are combined to the PCM-TD-DFT results. This study demonstrates that such a "hybrid" scheme, where the geometrical and vibrational parameters, as well as the solvation effects, are determined with PCM-TD-DFT, whereas the transition energies are obtained with a wavefunction-based method, offers a useful compromise between accuracy and computational cost.

Comparison of LC-TDDFT and ADC(2) Methods in Computations of Bright and Charge Transfer States in Stacked Oligothiophenes.

Long-range corrected time-dependent density functional theory (LC-TDDFT) has been applied to compute singlet vertical electronic excitations of oligothiophene molecules and their dimers and compared with the algebraic diagrammatic construction method to second order [ADC(2)], a wave function-based polarization propagator method. The excitation energies obtained from both methods agree to each other excellently. In particular, energetics of charge transfer states is concertedly reproduced. The linear response (LR) and the state specific (SS) approaches have been evaluated to appraise solvent effect on excited states. Benchmarked by the reference wave function method, the necessity of the SS treatment is justified in the prediction of charge transfer (CT) states under the TDDFT framework.

Optical Properties of Diarylethenes with TD-DFT: 0-0 Energies, Fluorescence, Stokes Shifts, and Vibronic Shapes.

This contribution is an investigation of both the structures and optical properties of a set of 14 diverse, recently synthesized diarylethenes using Time-Dependent Density Functional Theory (TD-DFT) at the ωB97X-D/6-31G(d) level of theory. The linear response (LR) and state-specific (SS) versions of the Polarizable Continuum Model (PCM) have been adopted to account for the bulk solvation effects and their relative performances were critically accessed. It is shown, for the first time in the case of nontrivial diarylethenes, that TD-DFT provides good agreement between the experimental absorption-fluorescence crossing points (AFCPs) and their theoretical counterparts when a robust model accounting for both geometrical relaxation and vibrational corrections is used instead of the vertical approximation. On the other hand, the theoretical estimates for the Stokes shifts based on the vertical transition energies were found to be in disagreement with respect to experiment, prompting us to simulate the absorption/emission vibronic band shapes. It is proved that difficulties associated with the breakdown of the harmonic approximation in Cartesian coordinates exist for the investigated system, and we show how they can be at least partially overcome by means of a vertical approach including Duschinsky effects. Our results provide a valuable basis to rationalize the experimental vibronic structure of both emission and absorption bands and are expected to be a significant asset to the understanding of the optical properties of diarylethene derivatives.

First-principle computation of absorption and fluorescence spectra in solution accounting for vibronic structure, temperature effects and solvent inhomogenous broadening

We compute the line shape of absorption and emission electronic spectra of two different dyes, Coumarin C153 and N-methyl-6-Quinolinium betaine accounting for the vibronic structure, temperature effects and polar solvent inhomogeneous broadening, without using any phenomenological parameter. We exploit a number of recent developments including a time-dependent (TD) approach to the computation of vibronic spectra that provides fully converged line shapes at finite temperature accounting for both Duschinsky and Herzberg–Teller effects, and the state-specific (SS) implementation of Polarizable Continuum Model (PCM). This latter is adopted to compute the solvent reorganization energy connected to inhomogenoeus broadening. We compute the absorption and fluorescence spectra in the gas-phase, non-polar and polar solvents analyzing the relative importance of different sources of broadening. To this end we investigate the performance of TD Density Functional Theory, Complete Active Space Self Consistent Field (CASSCF) and Complete Active Space second-order Perturbation Theory (CASPT2) methods in the computation of inhomogeneous broadening.

A corrected-linear response formalism for the calculation of electronic excitation energies of solvated molecules with the CCSD-PCM method

In this work, we present an efficient approximation to compute excitation energies in solution when coupled cluster (CC) methods are combined with a polarizable solvation model. Two formalisms exist to compute excited state energies with polarizable solvation models: state-specific (SS) and linear-response (LR). The former more accurately describes the solute–solvent polarization in the excited state, but is computationally intensive. The LR formalism is efficient, but lacks proper relaxation effects. An approximate method, called corrected-LR (cLR), was originally formulated in the context of time-dependent density functional theory and the polarizable continuum model of solvation (PCM), and was shown to be able to recover most of the relaxation contributions of the SS formalism at a cost similar to LR. We have expanded the cLR idea to CC theory, and introduced an extra approximation that further reduces the computational effort with negligible loss of accuracy. The test cases reported in this contribution clearly show that the cLR-CC-PCM method is able to estimate transition energies in very close agreement with the SS formalism at a cost that is similar (in fact, slightly smaller) than the LR formalism. The average SS–LR difference is of the order of 0.10–0.20eV for nonequilibrium calculations, and 0.30–0.55eV for equilibrium calculations. The SS–cLR average difference is, on the other hand, 0.01–0.02eV for nonequilibrium calculations, and 0.05–0.15eV for equilibrium calculations. Therefore, the cLR approach is a promising alternative for computing excited state energies in solution with computationally intensive CC methods.

Optical Signatures of OBO Fluorophores: A Theoretical Analysis.

Dioxaborines dyes, based on the OBO atomic sequence, constitute one promising series of molecules for both organic electronics and bioimaging applications. Using Time-Dependent Density Functional Theory, we have simulated the optical signatures of these fluoroborates. In particular, we have computed the 0-0 energies and shapes of both the absorption and the emission bands. To assess the importance of solvent effects three polarization schemes have been applied within the Polarizable Continuum Model: the linear-response (LR), the corrected linear-response (cLR), and the state-specific (SS). We show that the SS approach is unable to yield consistent chemical trends for these challenging compounds that combine charge-transfer and cyanine characters. On the contrary, LR and cLR are more effective in reproducing chemical trends in OBO dyes. We have applied our computational protocol not only to analyze the signatures of existing dyes but also to design structures with red-shifted absorption and emission bands.

Role of Solvent on Charge Transfer in 7-Aminocoumarin Dyes: New Hints from TD-CAM-B3LYP and State Specific PCM Calculations.

Time-dependent B3LYP and CAM-B3LYP calculations have been used to investigate the absorption and emission energies as well as to shed light on the formation of the twisted intramolecular charge transfer state (TICT) in Coumarin-152 (C152) embedded in cyclohexane, acetonitrile, and water solvents. The bulk solvent effects have been included by using the linear-response (LR) and State-Specific (SS) models in the framework of the so-called polarizable continuum method (PCM). The results demonstrate that the choice of the exchange-correlation functional and of the PCM model is critical to reproduce the experimental data in the most accurate way. In particular, it has been observed that both the solvatochromic and Stokes' shifts are well reproduce by CAM-B3LYP/SSPCM calculations performed on the S0 and S1 geometries of C152 optimized at the B3LYP/LRPCM level of theory, whereas not accurate Stokes' shifts are computed with CAM-B3LYP/SSPCM calculations carried out on the CAM-B3LYP/LRPCM optimized structures. This is attributed to the incorrect (underestimated) solvation energy provided by LRPCM, which could lead to misleading results especially for charge-transfer excited state structures in polar solvents. Instead, B3LYP/LRPCM excited state optimizations seem to provide a reasonable geometry for a simple 'error cancellation' effect due to the balance among the B3LYP overstabilization of charge transfer states and the LRPCM underestimation of the solute-solvent binding energy when the former is in a polar solvent. Finally, CAM-B3LYP/SSPCM calculations, in very good agreement with experimental evidence, show that the formation of an accessible TICT state is possible for C152 and that the crossing between S0 and S1 states at a dihedral angle of around 70° occurs only in polar solvents.

TD-DFT study of the [formula omitted] for coumarins

The excited state acid dissociation constants (pKa∗) of a panel of five coumarins have been studied using several PCM–TD-DFT protocols including both vibrational and state-specific (SS) effects. The pKa∗ have been calculated using the excited state thermodynamical cycle and the Förster cycle. For this set of compounds the addition of explicit water molecules does not improve the computed acidity constants computed with the thermodynamical cycle. However, the addition of explicit water molecules to the PCM model apparently improves the quality of the optical spectra and hence the Förster estimates. State specific effects do not bring significant improvements in this case.

A comparison between state-specific and linear-response formalisms for the calculation of vertical electronic transition energy in solution with the CCSD-PCM method

The calculation of vertical electronic transition energies of molecular systems in solution with accurate quantum mechanical methods requires the use of approximate and yet reliable models to describe the effect of the solvent on the electronic structure of the solute. The polarizable continuum model (PCM) of solvation represents a computationally efficient way to describe this effect, especially when combined with coupled cluster (CC) methods. Two formalisms are available to compute transition energies within the PCM framework: State-Specific (SS) and Linear-Response (LR). The former provides a more complete account of the solute-solvent polarization in the excited states, while the latter is computationally very efficient (i.e., comparable to gas phase) and transition properties are well defined. In this work, I review the theory for the two formalisms within CC theory with a focus on their computational requirements, and present the first implementation of the LR-PCM formalism with the coupled cluster singles and doubles method (CCSD). Transition energies computed with LR- and SS-CCSD-PCM are presented, as well as a comparison between solvation models in the LR approach. The numerical results show that the two formalisms provide different absolute values of transition energy, but similar relative solvatochromic shifts (from nonpolar to polar solvents). The LR formalism may then be used to explore the solvent effect on multiple states and evaluate transition probabilities, while the SS formalism may be used to refine the description of specific states and for the exploration of excited state potential energy surfaces of solvated systems.

Boranil and Related NBO Dyes: Insights From Theory.

The simulations of excited-state properties, that is, the 0-0 energies and vibronic shapes, of a large panel of fluorophores presenting a NBO atomic sequence have been achieved with a Time-Dependent Density Functional Theory (TD-DFT) approach. We have combined eight hybrid exchange-correlation functionals (B3LYP, PBE0, M06, BMK, M06-2X, CAM-B3LYP, ωB97X-D, and ωB97) to the linear-response (LR) and the state specific (SS) Polarizable Continuum Model (PCM) methods in both their equilibrium (eq) and nonequilibrium (neq) limits. We show that the combination of the SS-PCM scheme to a functional incorporating a low amount of exact exchange can yield unphysical values for molecules presenting large increase of their dipole moments upon excitation. We therefore apply a functional possessing a large exact exchange ratio to simulate the properties of NBO dyes, including large dyads.

Methodological keys for accurate simulations

Photoacids have a stronger propensity to give protons in their excited state than in their ground state which is a key feature for developing new material properties. Experimentally the determination of the excited state dissociation constants (pKa*) remains challenging as the lifetime of the photoacid, in its excited state, is too small. The present article establishes several protocols using the latest developments of the PCM-TD-DFT formalism e.g. both the corrected linear response (cLR) and state specific (SS) approaches. Equilibrium (eq) and non-equilibrium (neq) limits of the implicit solvent have been compared and we highlight that the SS-TD-DFT formalism provides figures in good agreement with experimental data once the eq limit is combined with the Born-Haber cycle or when the neq is used with the Föster cycle using absorption rather than emission transition energies.

Mechanisms for Solvatochromic Shifts of Free-Base Porphine Studied with Polarizable Continuum Models and Explicit Solute-Solvent Interactions.

Solvatochromic shifts of free-base porphine in the Q-band and B-band were studied using the polarizable continuum model (PCM) and explicit solvent molecules employing time-dependent density functional theory (TDDFT) and the symmetry-adapted cluster-configuration interaction (SAC-CI) method. The state-specific (SS) and linear-response (LR) methods were examined in the PCM calculations. These models involve different types of solute-solvent interactions. The LR PCM and explicit solvation models reproduced the experimentally observed trends of the solvatochromic shifts, while the SS PCM failed to reproduce the experimental findings. The origin of the solvatochromic shifts of free-base porphine was dispersive interactions between the solute and solvent. Specific solute-solvent interactions would be important for a decrease of the splitting width between Q-bands. Based on the Casimir-Polder formula and a decomposition analysis, it was found that the dominant part of the solute-solvent interactions can be considered using independent particle approximations.

Interplay between solvent models and predicted optical spectra: A TD-DFT study of 7-OH-coumarin

Using time-dependent density functional theory, we investigate the solvatochromic effects on the optical spectra of a typical hydroxy coumarin, considering its enol, keto, anionic and cationic forms. The absorption and fluorescence transitions energies have been computed within both the linear-response (LR) and the more refined state specific (SS) approaches, with explicit solvent molecules. These energies have also been used to compute 0–0 transitions and vibrationally resolved spectra. We show that the SS approach is mandatory to describe the solvent response due to the large increase of dipole moment upon the excitation while hydrogen bonds tune both absorption and emission energies.

MkMRCC, APUCC and APUBD approaches to 1,n-didehydropolyene diradicals: the nature of through-bond exchange interactions

Mukherjee-type (Mk) state specific (SS) multi-reference (MR) coupled-cluster (CC) calculations of 1,n-didehydropolyene diradicals were carried out to elucidate singlet-triplet energy gaps via through-bond coupling between terminal radicals. Spin-unrestricted Hartree–Fock (UHF) based coupled-cluster (CC) computations of these diradicals were also performed. Comparison between symmetry-adapted MkMRCC and broken-symmetry (BS) UHF-CC computational results indicated that spin-contamination error of UHF-CC solutions was left at the SD level, although it had been thought that this error was negligible for the CC scheme in general. In order to eliminate the spin contamination error, approximate spin-projection (AP) scheme was applied for UCC, and the AP procedure indeed eliminated the error to yield good agreement with MRCC in energy. The CCD with spin-unrestricted Brueckner's orbital (UB) was also employed for these polyene diradicals, showing that large spin-contamination errors at UHF solutions are dramatically improved, and therefore AP scheme for UBD removed easily the rest of spin-contaminations. Pure- and hybrid-density functional theory (DFT) calculations of the species were also performed. Three different computational schemes for total spin angular momentums were examined for the AP correction of the hybrid DFT. The AP DFT calculations yielded the singlet-triplet energy gaps that were in good agreement with those of MRCC, AP UHF-CC and AP UB-CC. Chemical indices such as the diradical character were calculated with all these methods. Implications of the present computational results are discussed in relation to previous RMRCC calculations of diradical species and BS calculations of large exchange coupled systems.

Accounting for the exact degeneracy and quasidegeneracy in the automerization of cyclobutadiene via multireference coupled-cluster methods

The automerization of cyclobutadiene (CBD) is employed to test the performance of the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (RMR CCSD) that employs a modest-size MR CISD wave function as an external source for the most important (primary) triples and quadruples in order to account for the nondynamic correlation effects in the presence of quasidegeneracy, as well as of its perturbatively corrected version accounting for the remaining (secondary) triples [RMR CCSD(T)]. The experimental results are compared with those obtained by the standard CCSD and CCSD(T) methods, by the state universal (SU) MR CCSD and its state selective or state specific (SS) version as formulated by Mukherjee et al. (SS MRCC or MkMRCC) and, wherever available, by the Brillouin-Wigner MRCC [MR BWCCSD(T)] method. Both restricted Hartree-Fock (RHF) and multiconfigurational self-consistent field (MCSCF) molecular orbitals are employed. For a smaller STO-3G basis set we also make a comparison with the exact full configuration interaction (FCI) results. Both fundamental vibrational energies-as obtained via the integral averaging method (IAM) that can handle anomalous potentials and automatically accounts for anharmonicity- and the CBD automerization barrier for the interconversion of the two rectangular structures are considered. It is shown that the RMR CCSD(T) potential has the smallest nonparallelism error relative to the FCI potential and the corresponding fundamental vibrational frequencies compare reasonably well with the experimental ones and are very close to those recently obtained by other authors. The effect of anharmonicity is assessed using the second-order perturbation theory (MP2). Finally, the invariance of the RMR CC methods with respect to orbital rotations is also examined.

A dual‐level state‐specific time‐dependent density‐functional theory

A highly efficient new algorithm for time-dependent density-functional theory (TDDFT) calculations is presented. In this algorithm, a dual-level approach to speed up DFT calculations (Nakajima and Hirao, J Chem Phys 2006, 124, 184108) is combined with a state-specific (SS) algorithm for TDDFT (Chiba et al., Chem Phys Lett 2006, 420, 391). The dual-level SS-TDDFT algorithm was applied to excitation energy calculations of typical small molecules, the Q bands of the chlorophyll A molecule, the charge-transfer energy of the zincbacteriochlorin-bacteriochlorin model system, and the lowest-lying excitation of the circumcoronene molecule. As a result, it was found that the dual-level SS-TDDFT gave correct excitation energies with errors of 0.2-0.3 eV from the standard TDDFT approach, with much lower CPU times for various types of excitation energies of large-scale molecules.

Toward effective and reliable fluorescence energies in solution by a new state specific polarizable continuum model time dependent density functional theory approach

A state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of emission energies has been developed and coded in the framework of the so called polarizable continuum model (PCM). The new model allows for a rigorous and effective treatment of dynamical solvent effects in the computation of fluorescence and phosphorescence spectra in solution, and it can be used for studying different relaxation time regimes. SS and conventional linear response (LR) models have been compared by computing the emission energies for different benchmark systems (formaldehyde in water and three coumarin derivatives in ethanol). Special attention is given to the influence of dynamical solvation effects on LR geometry optimizations in solution. The results on formaldehyde point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents and/or weak transitions. The computed emission energies for coumarin derivatives are very close to their experimental counterparts, pointing out the importance of a proper treatment of nonequilibrium solvent effects on both the excited and the ground state energies. The availability of SS-PCM/TD-DFT models for the study of absorption and emission processes allows for a consistent treatment of a number of different spectroscopic properties in solution.

A state-specific polarizable continuum model time dependent density functional theory method for excited state calculations in solution

An effective state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of excited electronic states has been developed and coded in the framework of the so-called polarizable continuum model (PCM). Different relaxation time regimes can be treated thus giving access to a number of different spectroscopic properties together with solvent relaxation energies of paramount relevance in electron transfer processes. SS and conventional linear response (LR) models have been compared for two benchmark systems (coumarin 153 and formaldehyde in different solvents) and in the limiting simple case of a dipolar solute embedded in a spherical cavity. The results point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents. The favorable scaling properties of PCM-TD-DFT models in both SS and LR variants and their availability in effective quantum mechanical codes pave the route for the computation of reliable spectroscopic properties of large molecules of technological and/or biological interest in their natural environments.

Electronic excitation energies of molecules in solution within continuum solvation models: Investigating the discrepancy between state-specific and linear-response methods

In a recent article [R. Cammi, S. Corni, B. Mennucci, and J. Tomasi, J. Chem. Phys. 122, 104513 (2005)], we demonstrated that the state-specific (SS) and the linear-response (LR) approaches, two different ways to calculate solute excitation energies in the framework of quantum-mechanical continuum models of solvation, give different excitation energy expressions. In particular, they differ in the terms related to the electronic response of the solvent. In the present work, we further investigate this difference by comparing the excitation energy expressions of SS and LR with those obtained through a simple model for solute-solvent systems that bypasses one of the basic assumptions of continuum solvation models, i.e., the use of a single Hartree product of a solute and a solvent wave function to describe the total solute-solvent wave function. In particular, we consider the total solute-solvent wave function as a linear combination of the four products of two solute states and two solvent electronic states. To maximize the comparability with quantum-mechanical continuum model the resulting excitation energy expression is recast in terms of response functions of the solvent and quantities proper for the solvated molecule. The comparison of the presented expressions with the LR and SS ones enlightens the physical meaning of the terms included or neglected by these approaches and shows that SS agrees with the results of the four-level model, while LR includes a term classified as dispersion in previous treatments and neglects another related to electrostatic. A discussion on the possible origin of the LR flaw is finally given.